Upload
mirit
View
44
Download
0
Tags:
Embed Size (px)
DESCRIPTION
An Implementation of Multiply Sectioned Bayesian Networks. Metron, Inc. Chris Boner Thor Whalen. Outline. Multiply sectioned Bayes nets (MSBN) Problem formulation and elements of a solution Using a junction tree to construct an MSBN Matlab tool. Multiply Sectioned Bayes Net. - PowerPoint PPT Presentation
Citation preview
1
An Implementation of Multiply An Implementation of Multiply Sectioned Bayesian NetworksSectioned Bayesian Networks
Metron, Inc.
Chris Boner
Thor Whalen
2
OutlineOutline
• Multiply sectioned Bayes nets (MSBN)
• Problem formulation and elements of a solution
• Using a junction tree to construct an MSBN
• Matlab tool
3
Multiply Sectioned Bayes NetMultiply Sectioned Bayes Net
• What is a Bayes Net?• What is a Multiply Sectioned Bayes Net (MSBN)?• Motivation
4
What is a Bayes Net?What is a Bayes Net?• A Bayes Net is a representation of
a probability distribution P(V) on a set V=X1, ..., Xn of variables
5
What is a Bayes Net?What is a Bayes Net?• A Bayes Net is a representation of
a probability distribution P(V) on a set V=X1, ..., Xn of variables
• A BN consists of – A Directed Acyclic Graph (DAG)
• Nodes: Variables of V
• Edges: Causal relations
A DAG is a directed graph with no directed cycles
The above directed graph is a DAG
Now this graph IS NOT a DAG because it has a directed cycle
Directed cycle
X1 X2 X3
X4 X5
X6
X7X8
X9 X10
X11 X12 X13
6
What is a Bayes Net?What is a Bayes Net?• A Bayes Net is a representation of
a probability distribution P(V) on a set V=X1, ..., Xn of variables
• A BN consists of – A Directed Acyclic Graph (DAG)
• Nodes: Variables of V
• Edges: Causal relations
– A list of conditional probability distributions (CPDs); one for every node of the DAG
X1 X2 X3
X4 X5
X6
X7X8
X9 X10
X11 X12 X13
Etc...
7
- i.e. P(A , B | C) = P(A | C) P(B | C)
What is a Bayes Net?What is a Bayes Net?• A Bayes Net is a representation of
a probability distribution P(V) on a set V=X1, ..., Xn of variables
• A BN consists of – A Directed Acyclic Graph (DAG)
• Nodes: variables of V
• Edges: Causal relations
– A list of conditional probability distributions (CPDs); one for every node of the DAG
• The DAG characterizes the (in)dependence structure of P(V)
X1 X2 X3
X4 X5
X6
X7X8
X9 X10
X11 X12 X13
A C
BA and are independent given
B
C
- i.e. P(A | B, C) = P(A | C)
We will say that C separates A and B
8
What is a Bayes Net?What is a Bayes Net?• A Bayes Net is a representation of
a probability distribution P(V) on a set V=X1, ..., Xn of variables
• A BN consists of – A Directed Acyclic Graph (DAG)
• Nodes: variables of V
• Edges: Causal relations
– A list of conditional probability distributions (CPDs); one for every node of the DAG
• The DAG characterizes the (in)dependency structure of P(V)
• The CPDs characterize the probabilistic and/or deterministic relations between parent states and children states
X1 X2 X3
X4 X5
X6
X7X8
X9 X10
X11 X12 X13
9
X7
X3X1 X2
X5
X8
X4
X11 X13
X6
X7
X12Evidence
What is a Bayes Net?What is a Bayes Net?
• The prior distributions on the variables of parentless nodes, along with the CPDs of the BN, induce prior distribution—called “beliefs” in the literature—on all the variables
• If the system receives evidence on a variable: – this evidence impacts its belief,– along with the beliefs of all other
variables
X9 X10
Parentless nodes
10
• Subnets of the BN are maintained independently
• Each subnet locally integrates evidence it receives
• When inter-subnets communication is possible, messages are passed that enable fusion of evidence received by other subnets
Evidence
Evidence
What is a Multiply Sectioned Bayes Net?What is a Multiply Sectioned Bayes Net?
11
• Multi-agent systems where:– each agent only has partial knowledge of the
domain– communication among agents is limited
• some agent-agent connections may be impossible, sporadic and/or low bandwidth
– decisions must be made by agents based on local observations and limited information from other agents
MotivationMotivation
12
Motivation (2)Motivation (2)
• Distributed computing for reusable systems where:– probabilistic knowledge can be captured once
and used for multiple cases– queries and evidence will be localized, that is,
there are phases when• new evidence and queries are repeatedly directed
to small parts of network• only a small part of the network is needed for
decision-making
13
• Problem specification
• A naïve solution
• A less naïve solution
• Sufficient information
• Communication graph considerations
Problem Formulation Problem Formulation and elements of a solutionand elements of a solution
14
Problem SpecificationProblem SpecificationGiven: • A BN on V={X1, ..., Xn}
• A number of agents, each having:– Qi: a set of query variables
– Ei: a set of evidence variables
15
Problem SpecificationProblem SpecificationGiven: • A BN on V={X1, ..., Xn}
• A number of agents, each having:– Qi: a set of query variables
– Ei: a set of evidence variables
Determine: • An agent communication graph
• A subset Si of V for each agent
• An inference protocol that specifies – How to fuse evidence and messages
received from other agents– The content of messages between
agents
16
Every agent has a copy of the entire Bayes net
Evidence
Agents communicate evidence (findings or likelihood functions) that are re-propagated through each copy of the BN
A Naïve SolutionA Naïve Solution
17
Pros• Each agent’s queries
are as informed as possible once all the evidence it has received is propagated
• Inter-agent communications require relatively low bandwidth
Cons• Could be a colossal
waste of memory and processing time
• Each agent may be able to achieve fully informed queries by representing a much smaller section of BN
A Naïve SolutionA Naïve Solution
18
• The previous solution allows each agent to compute the posterior prob. of all the variables
• But all the agent is interested in is the posterior of its query variables
• Hence it is sufficient for every agent to only represent
- its query variables, - its evidence variables, - the evidence variables
of the other agents• Contra: Could be a
colossal waste of memory and processing time
A Less Naïve SolutionA Less Naïve Solution
Query
variables
Query
variables
Query
variables
Query
variables
Evidence
variables
Evidence
variables
Evidence
variables
Evidence
variables
19
Sufficient informationSufficient information
B
CD
A
E
F
GH
I
JK
L
M
Evidence variables
Query variables
Agent 1
Agent 2
Agent 3
Agent 4
Specifications
• A Bayes net
• A number of agents, each having
- query variables
- evidence variables
20
Sufficient informationSufficient information
B
CD
A
E
F
GH
I
JK
L
M
Agent 1
E F G
H I J
K L M
E F G
H I J
K L M
A B
E F G K L MH I J
Specifications
• A Bayes net
• A number of agents, each having
- query variables
- evidence variables
Agent 2
Agent 3
Agent 4
The naïve solution
• Agents contain their own query and evidence variables
• In order to receive evidence from the other agents, agent 1 must represent variables E, F, G, H, I, J, K, L, and M
Agent 1
Agent 2 Agent 3 Agent 4
21
E F G K L MH I J
Sufficient informationSufficient information
B
CD
A
E
F
GH
I
JK
L
M
Agent 1
E F G K L MH I J
A B
Specifications
• A Bayes net
• A number of agents, each having
- query variables
- evidence variables
Agent 2
Agent 3
Agent 4
The naïve solution
• Agents contain their own query and evidence variables
• In order to receive evidence from the other agents, agent 1 must represent variables E, F, G, H, I, J, K, L, and M
Y
ZX
separatesZ and X Y
Note that
whether Y is equal to:
• {K,L,M},
• {H,J,I}, or
• {E,F,G}.YY
Agent 1 must
represent many
variables!
How else could
the other agents
communicate their
evidence?
22
P(X,Z|eY)
Sufficient informationSufficient information
B
C D
A
E
F
G
separatesZ and X Y
Z
X
Y
X = {A,B}
Z = {C,D}
Z = {C,D}
Y = {E,G,F}
P(Y|Z) = P(Y|X,Z)
→→
Likelihood given X and Z
of evidence on Y
Likelihood given Z
of evidence on Y=
→ It is sufficient for agent 2 to send its posterior on Z
to agent 1 for the latter to compute its posterior on X
Agent 1
Agent 2
P(Y,Z|eY)
P(X,Z)
P(Z|eY)
P(Y,Z)
ΣY
x P(X,Z)P(Z)-1
evidence eY
23
P(X,Z|eY)
Sufficient informationSufficient information
B
C D
A
E
F
G
separatesZ and X Y
Z
X
Y
X = {A,B}
Z = {C,D}
Z = {C,D}
Y = {E,G,F}
P(Y|X,Z) = P(Y|Z)
→→
Likelihood given X and Z
of evidence on Y
Likelihood given Z
of evidence on Y=
→ It is sufficient for agent 2 to send its posterior on Z
to agent 1 for the latter to compute its posterior on X
Agent 1
Agent 2
P(Y,Z|eY)
P(Z|eY)
P(eY)-1
P(Z)-1P(X,Z) P(Z|eY)
P(Z)-1= P(X,Z) P(Z,eY)
P(eY)-1= P(X,Z) P(eY|Z)
P(eY)-1= P(X,Z) P(eY|X,Z)
P(X,Z|eY)P(eY)-1= P(X,Z,eY) =
Because:
P(eY|Z)P(eY|X,Z)
24
E F G K L MH I J
Sufficient informationSufficient information
E F G K L MH I J
A B
Specifications
• A Bayes net
• A number of agents, each having
- query variables
- evidence variables
The naïve solution
• Agents contain their own query and evidence variables
• In order to receive evidence from the other agents, agent 1 must represent variables E, F, G, H, I, J, K, L, and M
C D
E F G K L MH I J
A B
C D C D C D
Using separation
• Agent 1 only needs to represent two extra variables
• Agent 1 may compute its posterior queries faster from CD than from EFGHIJK
• Communication lines need to transmit two variables instead of three
E F G K L MH I JE F G K L MH I J
C D C D C DC D C D C D
25
Communication Graph ConsiderationsCommunication Graph Considerations
1
2
3
4
5
6
Agent 6 receives info from agent 1 through both agent 4 and 5.
How should subnet 6 deal with possible redundancy?
A communication graphOne solution (often adopted) would be to impose a tree structure to the communication graph
26
Communication Graph ConsiderationsCommunication Graph Considerations
• When choosing the communication graph, one should take into consideration
- The quality of the possible communication lines- The processing speed of the agents- The importance of given queries
If this is the key decision-making agent
...then this communication graph is more appropriate… than this one
27
• In a tree communication graph every edge is the only communication line
between two parts of the network• Hence it must deliver enough information so that the evidence received in
one part may convey its impact to the query variables of the other part• We restrict ourselves to the case where every node represented by an agent can be queried or receive evidence• In this case it is sufficient that the set of variables Z, that will be represented in any communication line, separates the set X of variables of one side of the network from the set Y of variables of the other side
Communication Graph ConsiderationsCommunication Graph Considerations
Z
YX
28
Using a Junction Tree Using a Junction Tree to construct an MSBNto construct an MSBN
• The junction tree and its use• Building a Junction tree
– Moralization– Triangulation– The junction graph– From junction graph to junction tree
• Partitioning the junction tree• Adding and removing agents• A note on continuous variables
29
a
b c
d e
f
g
h
Secondary Structure/Junction Tree• multi-dim. random variables• joint probabilities (potentials)
Bayesian Network• one-dim. random variables• conditional probabilities
abd
ade
ace
ceg
eghdef
ad ae ce
de eg
The junction tree and its useThe junction tree and its use
30
abd
ade
ace
ceg
eghdef
• A junction tree is a graphical model of a probability space:
- Nodes of a JT are sets of variables
- Edges of a JT (called sepsets) are labeled by the intersection of the set of variables of the nodes they join
• The set of variables Z of any edge of a JT separates the set of variables of the sub-trees of both sides of this edge
ad
de
ae ce
eg
e.g.{a,e} separates {a,b,d,e,f} and {a,c,e,g,h}
a
b c
d e
f
g
h
The junction tree and its useThe junction tree and its use
31
abd
ade
ace
ceg
eghdef
ad
de
ae ce
eg
The junction tree and its useThe junction tree and its use
So any partition a junction tree into sub-trees will allow for distributed inference
a
b
d e
f
a
c
e
g
e
g
h
a,e
e,g
32
TopCat
Feat 3Feat 7 Feat 8
Feat 5Feat 4
Feat 6
Feat 1 Feat 2
Sens1b
Sens1a
Sens2b
Sens2a
Example of the Junction Tree ApproachExample of the Junction Tree Approach
Agent 1
Agent 2
Agent 2
Agent 4
query nodes
query nodes
evidence nodes
query nodesevidence nodes
query nodes
evidence nodes
33
Building a Junction TreeBuilding a Junction Tree
DAG
Moral Graph
Triangulated Graph
Junction Tree
Identifying Cliques
a
b c
d e
f
g
h a
b c
d e
f
g
ha
b c
d e
f
g
h a
b
d
a
c
ed e
f
a
d e
c
e
g
e
g
h
34
TopCat
Feat 3Feat 7 Feat 8
Feat 5Feat 4
Feat 6
Feat 1 Feat 2
Sens1b
Sens1a
Sens2b
Sens2a
Building a Junction TreeBuilding a Junction Tree: MoralizationMoralization
1) Add an edge between every node having a common child.
2) Drop the directions of all other edges.
35
TopCat
Feat 3Feat 7 Feat 8
Feat 5Feat 4
Feat 6
Feat 1 Feat 2
Sens1b
Sens1a
Sens1b
Sens1a
Building a Junction TreeBuilding a Junction Tree: TriangulationTriangulation
Add edges to the graph to triangulate (induced) cycles of length greater than three.
This is the only
induced cycle
of length greater
than three
There are only two ways
to triangulate it...So we’ll choose this
way for our example
This way can be shown
to be problematic
36
Building a Junction TreeBuilding a Junction Tree: Junction GraphJunction Graph
TopCat
Feat 3Feat 7 Feat 8
Feat 5Feat 4
Feat 6
Feat 1 Feat 2
Sens1b
Sens1a
Sens2b
Sens2a
• A complete subgraph is one with edges between every vertex of the subgraph.
• A clique is a complete subgraph contained in no other complete subgraph.
This is a clique.This is a clique.
This is NOT a clique.Now it IS a clique.
37
Building a Junction TreeBuilding a Junction Tree: Junction GraphJunction Graph
TopCat
Feat 3
Feat 7Feat 8
Feat 4
Feat 6
Feat 1 Feat 2
Sens1b
Sens1a
Sens2b
1) Identify Cliques.Every clique corresponds to a node in the JG.
3) Label edges of JG with intersection of cliques.
Feat 1 Feat 2Sens1aSens1b
Feat 5 Feat 6Sens2aSens2b
Feat 1Feat 2TopCat
Feat 5Feat 4Feat 3
Feat 4Feat 7
TopCat
Feat 4Feat 3TopCat Feat 8
Feat 7TopCat
Feat 4
Feat 8Feat 7
2) Draw an edge between two nodes if they share variables.
Feat 1Feat 2
TopCatTopCat
TopCat
Feat 8Feat 7
Feat 4
Feat 3Feat 4
Feat 4
Feat 4
Feat 4TopCat
Feat
7
Feat 5
Feat 7
Feat 5
Sens2a
TopC
at
38
Feat 1 Feat 2
Sens1a Sens1b Feat 5 Feat 6
Sens2a Sens2b
Feat 1
Feat 2
TopCat
Feat 5
Feat 4
Feat 3
Feat 4
Feat 7
TopCat
Feat 4
Feat 3
TopCat Feat 8
Feat 7
TopCat
Feat 4
Feat 8
Feat 7
Feat 4
From Junction Graph to Junction TreeFrom Junction Graph to Junction Tree
1
1
1
21
2
1
2
1
2
1) Weight every edge with the number of variables it is labeled with
2) Find a maximal weight spanning (i.e. covering all JG nodes) tree
3) The corresponding subgraph of the JG is a Junction Tree (JT)
Feat 2
TopCatTopCat
TopCat
Feat 8
Feat 4
TopCat
Feat 5
2
2
Feat 1
Feat 4
Feat 4
Feat 7
Feat 4
Feat 7
Feat 7TopCat
Feat 3
The cliques are
the nodes of the JT
The edges of the JT
are called sepsets
39
Feat 1 Feat 2
Sens1a Sens1b
Feat 5 Feat 6
Sens2a Sens2b
Feat 1
Feat 2
TopCat
Feat 5
Feat 4
Feat 3
Feat 4
Feat 7
TopCat
Feat 4
Feat 3
TopCat
Feat 8
Feat 7
TopCat
Feat 4
Feat 8
Feat 7
TopCatTopCat
Feat 4
Feat 4
TopCat
Partitioning the Junction TreePartitioning the Junction Tree
• Partition the nodes of the JT:
Sets of the partition → subnets
• Edges between two nodes of different subnets → communication lines
• Desirable for portion of JT inside a subnet to be connected
Feat 1
Feat 2Feat 5
Feat 8
Feat 7
Feat 3
40
Corresponding SubnetsCorresponding Subnets
TopCat
Feat 3
Feat 7 Feat 8Feat 5
Feat 4
Feat 1 Feat 2
Feat 1 Feat 2 Feat 5
Feat 6
Feat 7 Feat 8
Feat 1 Feat 2 Feat 5
Feat 7 Feat 8
Evidence EvidenceEvidence
TopCat
Feat 3
Feat 7 Feat 8Feat 5
Feat 4
Feat 1 Feat 2
Sens1b
Sens1a Feat 6
Sens2b
Sens2a
Feat 4
Partitioning the Junction TreePartitioning the Junction Tree
41
Adding and removing AgentsAdding and removing Agents
TopCat
Feat 3Feat 7 Feat 8
Feat 5Feat 4
Feat 6
Feat 1 Feat 2
Sens1b
Sens1a
Sens2b
Sens2a
Sens3b
Sens3a
Sens5b
Sens5a
Sens4b
Sens4a
Sens6b
Sens6a
• Here we address the problem of adding and removing agents to the network
• Consider the BN given earlier
• Is it possible to add and remove agents (containing sensor variables) to the
network and perform inference without reconfiguring the network
42
Adding and removing Agents (2)Adding and removing Agents (2)
TopCat
Feat 1 Feat 2
Sens1b
Sens1a
Sens3b
Sens3a
Sens5b
Sens5a
• Adding the cliques containing the new variables does not change the structure of the Junction tree, so new agents containing these variables may easily be added and removed, along with a single communication line to the rest of the network.
Etc ...
Feat 1 Feat 2
Sens3a Sens3b
Feat 1
Feat 2
TopCat
Feat 1 Feat 2
Sens5a Sens5b
Feat 1 Feat 2
Sens1a Sens1b
Feat 2
Feat 1
Feat 2
Feat 1
Feat 2
Feat 1
Etc ...
43Feat 5
Feat 6
Feat 5
Feat 6
Adding and removing Agents (3)Adding and removing Agents (3)
• Adding the cliques containing the new variables does not change the structure of the Junction tree, so new agents containing these variables may easily be added and removed, along with a single communication line to the rest of the network.
TopCat
Feat 3
Feat 7 Feat 8
Feat 5
Feat 4
Feat 6Sens2b
Sens2a
Sens6b
Sens6a
Sens4b
Sens4a
Etc ...
Feat 5 Feat 6
Sens2a Sens2b
Feat 5
Feat 4
Feat 3
Feat 4
Feat 7
TopCat
Feat 4
Feat 3
TopCat
Feat 8
Feat 7
TopCat
Feat 4
TopCat
Feat 5
Feat 4Feat 7
TopCatFeat 3
Feat 5 Feat 6
Sens4a Sens4b
Feat 5 Feat 6
Sens6a Sens6b
Etc ...
44Feat 5
Feat 6
Feat 5
Feat 6
Adding and removing Agents (4)Adding and removing Agents (4)
• It is not desirable to have sensors chained as such since evidence received in one agent must pass through other agents to reach the central agent
• It would be preferable to have the sensor agents communicate with the central agent directly
TopCat
Feat 3
Feat 7 Feat 8
Feat 5
Feat 4
Feat 6Sens2b
Sens2a
Sens6b
Sens6a
Sens4b
Sens4a
Etc ...
Feat 5 Feat 6
Sens2a Sens2b
Feat 5
Feat 4
Feat 3
Feat 4
Feat 7
TopCat
Feat 4
Feat 3
TopCat
Feat 8
Feat 7
TopCat
Feat 4
TopCat
Feat 5
Feat 4Feat 7
TopCatFeat 3
Feat 5 Feat 6
Sens4a Sens4b
Feat 5 Feat 6
Sens6a Sens6b
Etc ...
45
Adding and removing Agents (3)Adding and removing Agents (3)
TopCat
Feat 3
Feat 7 Feat 8
Feat 5
Feat 4
Feat 6Sens2b
Sens2a
Sens6b
Sens6a
Sens4b
Sens4a
Etc ...
Feat 5 Feat 6
Sens2a Sens2b
Feat 5
Feat 4
Feat 3
Feat 4
Feat 7
TopCat
Feat 4
Feat 3
TopCat
Feat 8
Feat 7
TopCat
Feat 4
TopCat
Feat 5
Feat 4Feat 7
TopCatFeat 3
Feat 5 Feat 6
Sens4a Sens4b
Feat 5 Feat 6
Sens6a Sens6b
Etc ...
• By adding an extra variable the appropriate clique, we now have a different junction tree structure more fit for our application
Feat 5Feat 6
Feat 5Feat 6
Feat 6
Feat 6
46
A note on continuous variablesA note on continuous variables
• Wish to extend JT inference to handle continuous variables.
• JT inference ↔ Potential manipulation• In general, a potential Φ on X=X1, ..., Xn is
a function Φ: X1 x ... x Xn → [0,+∞)• We need to define
– Multiplication (and division) of two potentials• Use function multiplication for this
– marginalization of a potential• use integration instead of summation
47
• Prior distributions and all possible evidence likelihood functions must be represented algebraically by a class of functions closed under multiplication and integration
• If the class of functions doesn’t encompass the prior distributions and evidence exactly, the question arises whether approximate inference or discretization might yield better results
A note on continuous variablesA note on continuous variables
48
• Algebraic manipulation is not a straightforward computational task
• Exact integration is not always possible
• Is numerical integration necessarily better than approximate inference or discretization?
A note on continuous variablesA note on continuous variables
49
MatLab ToolMatLab Tool
• Setup
• Functionality
• Adding and removing subnets
50
>> setBN('benzene.dne')
The global BN is now "benzene.dne".
The CPDs are:------------------ ------------------------ ------------------------| P(A) | | P(C|A) | | P(B|A) | |----------------| |----------------------| |----------------------| | A | Values | | A C | Values | | A B | Values | |----------------| |----------------------| |----------------------| | True | 0.3000 | | True True | 0.7500 | | True True | 1.0000 | | False | 0.7000 | | True False | 0.2500 | | True False | 0.0000 | ------------------ | False True | 0.1000 | | False True | 0.3000 |
| False False | 0.9000 | | False False | 0.7000 | ------------------------ ------------------------
------------------------ ------------------------ ------------------------------| P(E|C) | | P(D|B) | | P(F|D,E) | |----------------------| |----------------------| |----------------------------| | C E | Values | | B D | Values | | E D F | Values | |----------------------| |----------------------| |----------------------------| | True True | 0.2000 | | True True | 0.2500 | | True True True | 0.1000 | | True False | 0.8000 | | True False | 0.7500 | | True True False | 0.9000 | | False True | 0.6000 | | False True | 0.3000 | | True False True | 0.3000 | | False False | 0.4000 | | False False | 0.7000 | | True False False | 0.7000 | ------------------------ ------------------------ | False True True | 0.2000 |
| False True False | 0.8000 | Description of cliques: | False False True | 0.4000 | Clique 1 has nodes A, C, B. | False False False | 0.6000 | Clique 2 has nodes C, B, E. ------------------------------Clique 3 has nodes B, E, D.Clique 4 has nodes E, D, F.
MatLab ToolMatLab Tool
• Bayes Net
– variables and states
– CPDs
– entered as simple text format or translated from a .dne Netica file
• Junction tree from Bayes Net
– entered as simple text format or translated from a .dne Netica file
• Partition of the junction tree
Inputs
51
i + [Enter] to Initialize, v + [Enter] to view all variables (even those
containing no information),e + [Enter] to enter evidence, c + [Enter] to perform a inter-subnet
communication,p + [Enter] to go to the previous step, n + [Enter] to go to the next step,a + [Enter] to add a sensor, r + [Enter] to remove a sensor,t + [Enter] to turn true marginals view ON, m + [Enter] to turn discrepancy marking OFF,s + [Enter] to save to a file, q + [Enter] to quit.
Enter Command:
MatLab ToolMatLab Tool
• Insert evidence into given subnets and propagate their impact inside the subnet
• Initiate communication between subnets, followed by the propagation of new information
• View the marginal distributions of the different subnets at every step
• Step forward and backward• Save eye-friendly logs to a
file
Main functionality
52
MatLab Tool: DisplayMatLab Tool: Display* Configuration 2: After evidence L(e|C) = (2,5) has been entered into subnet number 2
The TRUTH:------------------ ------------------ ------------------ ------------------ ------------------ ------------------| A | Values | | C | Values | | B | Values | | E | Values | | D | Values | | F | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.2005 | | True | 0.1434 | | True | 0.4403 | | True | 0.5426 | | True | 0.2780 | | True | 0.2901 | | False | 0.7995 | | False | 0.8566 | | False | 0.5597 | | False | 0.4574 | | False | 0.7220 | | False | 0.7099 | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 1 (adjacent to subnets 2): Err(ACB) = 0.0527.~~~~ AD = 0.0704 / ~~~~ AD = 0.1072 / ~~~~ AD = 0.0493 / ------------------ ------------------ ------------------/ A / Values / / C / Values / / B / Values / | E | Values | | D | Values | | F | Values | /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ |----------------| |----------------| |----------------| / True / 0.3000 / / True / 0.2950 / / True / 0.5100 / | True | ###### | | True | ###### | | True | ###### | / False / 0.7000 / / False / 0.7050 / / False / 0.4900 / | False | ###### | | False | ###### | | False | ###### | ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1, 3):------------------ ------------------ ------------------ ------------------ ------------------ ------------------| A | Values | | C | Values | | B | Values | | E | Values | | D | Values | | F | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | ###### | | True | 0.1434 | | True | 0.4403 | | True | 0.5426 | | True | 0.2780 | | True | ###### | | False | ###### | | False | 0.8566 | | False | 0.5597 | | False | 0.4574 | | False | 0.7220 | | False | ###### | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 2): Err(EDF) = 0.0169.------------------ ------------------ ------------------ ~~~~ AD = 0.0429 / ~~~~ AD = 0.0025 / ~~~~ AD = 0.0048 / | A | Values | | C | Values | | B | Values | / E / Values / / D / Values / / F / Values / |----------------| |----------------| |----------------| /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ | True | ###### | | True | ###### | | True | ###### | / True / 0.4820 / / True / 0.2745 / / True / 0.2969 / | False | ###### | | False | ###### | | False | ###### | / False / 0.5180 / / False / 0.7255 / / False / 0.7031 / ------------------ ------------------ ------------------ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
Enter a command (enter h + [Enter] for help):
Indicates step number and last action that was taken
Shows the marginal distributions that would have been obtained by infering on the entire Bayes Net
Shows the marginal distributions of the variables represented in each subnet
Prompts for new action
53
MatLab Tool: DisplayMatLab Tool: Display* Configuration 2: After evidence L(e|C) = (2,5) has been entered into subnet number 2
The TRUTH:------------------ ------------------ ------------------ ------------------ ------------------ ------------------| A | Values | | C | Values | | B | Values | | E | Values | | D | Values | | F | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.2005 | | True | 0.1434 | | True | 0.4403 | | True | 0.5426 | | True | 0.2780 | | True | 0.2901 | | False | 0.7995 | | False | 0.8566 | | False | 0.5597 | | False | 0.4574 | | False | 0.7220 | | False | 0.7099 | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 1 (adjacent to subnets 2): Err(ACB) = 0.0527.~~~~ AD = 0.0704 / ~~~~ AD = 0.1072 / ~~~~ AD = 0.0493 / ------------------ ------------------ ------------------/ A / Values / / C / Values / / B / Values / | E | Values | | D | Values | | F | Values | /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ |----------------| |----------------| |----------------| / True / 0.3000 / / True / 0.2950 / / True / 0.5100 / | True | ###### | | True | ###### | | True | ###### | / False / 0.7000 / / False / 0.7050 / / False / 0.4900 / | False | ###### | | False | ###### | | False | ###### | ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1, 3):------------------ ------------------ ------------------ ------------------ ------------------ ------------------| A | Values | | C | Values | | B | Values | | E | Values | | D | Values | | F | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | ###### | | True | 0.1434 | | True | 0.4403 | | True | 0.5426 | | True | 0.2780 | | True | ###### | | False | ###### | | False | 0.8566 | | False | 0.5597 | | False | 0.4574 | | False | 0.7220 | | False | ###### | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 2): Err(EDF) = 0.0169.------------------ ------------------ ------------------ ~~~~ AD = 0.0429 / ~~~~ AD = 0.0025 / ~~~~ AD = 0.0048 / | A | Values | | C | Values | | B | Values | / E / Values / / D / Values / / F / Values / |----------------| |----------------| |----------------| /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ | True | ###### | | True | ###### | | True | ###### | / True / 0.4820 / / True / 0.2745 / / True / 0.2969 / | False | ###### | | False | ###### | | False | ###### | / False / 0.5180 / / False / 0.7255 / / False / 0.7031 / ------------------ ------------------ ------------------ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
Enter a command (enter h + [Enter] for help): Indicates that subnet does not represent this variable
Indicates that marginal variable distribution matches “true marginal”
Indicates that marginal variable distribution differs from “true marginal”
Shows average discrapancy between subnet marginals and “true marginals”
Shows average discrepancy between subnet and true joint distributions of the variables of the subnet
54
MatLab ToolMatLab Tool
• Bayes Net
– variables and states
– CPDs
– entered as simple text format or translated from a .dne Netica file
• Junction tree from Bayes Net
– entered as simple text format or translated from a .dne Netica file
• Partition of the junction tree
>> setBN('benzene.dne')
The global BN is now "benzene.dne".
The CPDs are: ------------------ ------------------------ ------------------------ | P(A) | | P(C|A) | | P(B|A) | |----------------| |----------------------| |----------------------| | A | Values | | A C | Values | | A B | Values | |----------------| |----------------------| |----------------------| | True | 0.3000 | | True True | 0.7500 | | True True | 1.0000 | | False | 0.7000 | | True False | 0.2500 | | True False | 0.0000 | ------------------ | False True | 0.1000 | | False True | 0.3000 | | False False | 0.9000 | | False False | 0.7000 | ------------------------ ------------------------
------------------------ ------------------------ ------------------------------ | P(E|C) | | P(D|B) | | P(F|D,E) | |----------------------| |----------------------| |----------------------------| | C E | Values | | B D | Values | | E D F | Values | |----------------------| |----------------------| |----------------------------| | True True | 0.2000 | | True True | 0.2500 | | True True True | 0.1000 | | True False | 0.8000 | | True False | 0.7500 | | True True False | 0.9000 | | False True | 0.6000 | | False True | 0.3000 | | True False True | 0.3000 | | False False | 0.4000 | | False False | 0.7000 | | True False False | 0.7000 | ------------------------ ------------------------ | False True True | 0.2000 | | False True False | 0.8000 | Description of cliques: | False False True | 0.4000 | Clique 1 has nodes A, C, B. | False False False | 0.6000 | Clique 2 has nodes C, B, E. ------------------------------ Clique 3 has nodes B, E, D.Clique 4 has nodes E, D, F.
Inputs
55
i + [Enter] to Initialize,
v + [Enter] to view all variables (even those containing no information),
e + [Enter] to enter evidence,
c + [Enter] to perform a inter-subnet communication,
p + [Enter] to go to the previous step,
n + [Enter] to go to the next step,a + [Enter] to add a sensor,
r + [Enter] to remove a sensor,t + [Enter] to turn true marginals view ON,
m + [Enter] to turn discrepancy marking
OFF,s + [Enter] to save to a file,
q + [Enter] to quit.
Enter Command:
MatLab ToolMatLab Tool
• Insert evidence into given subnets and propagate their impact inside the subnet
• Initiate communication between subnets, followed by the propagation of new information
• View the marginal distributions of the different subnets at every step
• Step forward and backward• Save eye-friendly logs to a
file
Main functionality
56
MatLab Tool: DisplayMatLab Tool: Display * Configuration 2: After evidence L(e|C) = (2,5) has been entered into subnet number 2
The TRUTH:
------------------ ------------------ ------------------ ------------------ ------------------ ------------------
| A | Values | | C | Values | | B | Values | | E | Values | | D | Values | | F | Values |
|----------------| |----------------| |----------------| |----------------| |----------------| |----------------|
| True | 0.2005 | | True | 0.1434 | | True | 0.4403 | | True | 0.5426 | | True | 0.2780 | | True | 0.2901 |
| False | 0.7995 | | False | 0.8566 | | False | 0.5597 | | False | 0.4574 | | False | 0.7220 | | False | 0.7099 |
------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 1 (adjacent to subnets 2): Err(ACB) = 0.0527.
~~~~ AD = 0.0704 / ~~~~ AD = 0.1072 / ~~~~ AD = 0.0493 / ------------------ ------------------ ------------------
/ A / Values / / C / Values / / B / Values / | E | Values | | D | Values | | F | Values |
/~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ |----------------| |----------------| |----------------|
/ True / 0.3000 / / True / 0.2950 / / True / 0.5100 / | True | ###### | | True | ###### | | True | ###### |
/ False / 0.7000 / / False / 0.7050 / / False / 0.4900 / | False | ###### | | False | ###### | | False | ###### |
~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1, 3):
------------------ ------------------ ------------------ ------------------ ------------------ ------------------
| A | Values | | C | Values | | B | Values | | E | Values | | D | Values | | F | Values |
|----------------| |----------------| |----------------| |----------------| |----------------| |----------------|
| True | ###### | | True | 0.1434 | | True | 0.4403 | | True | 0.5426 | | True | 0.2780 | | True | ###### |
| False | ###### | | False | 0.8566 | | False | 0.5597 | | False | 0.4574 | | False | 0.7220 | | False | ###### |
------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 2): Err(EDF) = 0.0169.
------------------ ------------------ ------------------ ~~~~ AD = 0.0429 / ~~~~ AD = 0.0025 / ~~~~ AD = 0.0048 /
| A | Values | | C | Values | | B | Values | / E / Values / / D / Values / / F / Values /
|----------------| |----------------| |----------------| /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/
| True | ###### | | True | ###### | | True | ###### | / True / 0.4820 / / True / 0.2745 / / True / 0.2969 /
| False | ###### | | False | ###### | | False | ###### | / False / 0.5180 / / False / 0.7255 / / False / 0.7031 /
------------------ ------------------ ------------------ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
Enter a command (enter h + [Enter] for help):
Indicates step number and last action that was taken
Shows the marginal distributions that would have been obtained by infering on the entire Bayes Net
Shows the marginal distributions of the variables represented in each subnet
Prompts for new action
57
MatLab Tool: DisplayMatLab Tool: Display * Configuration 2: After evidence L(e|C) = (2,5) has been entered into subnet number 2
The TRUTH:
------------------ ------------------ ------------------ ------------------ ------------------ ------------------
| A | Values | | C | Values | | B | Values | | E | Values | | D | Values | | F | Values |
|----------------| |----------------| |----------------| |----------------| |----------------| |----------------|
| True | 0.2005 | | True | 0.1434 | | True | 0.4403 | | True | 0.5426 | | True | 0.2780 | | True | 0.2901 |
| False | 0.7995 | | False | 0.8566 | | False | 0.5597 | | False | 0.4574 | | False | 0.7220 | | False | 0.7099 |
------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 1 (adjacent to subnets 2): Err(ACB) = 0.0527.
~~~~ AD = 0.0704 / ~~~~ AD = 0.1072 / ~~~~ AD = 0.0493 / ------------------ ------------------ ------------------
/ A / Values / / C / Values / / B / Values / | E | Values | | D | Values | | F | Values |
/~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ |----------------| |----------------| |----------------|
/ True / 0.3000 / / True / 0.2950 / / True / 0.5100 / | True | ###### | | True | ###### | | True | ###### |
/ False / 0.7000 / / False / 0.7050 / / False / 0.4900 / | False | ###### | | False | ###### | | False | ###### |
~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1, 3):
------------------ ------------------ ------------------ ------------------ ------------------ ------------------
| A | Values | | C | Values | | B | Values | | E | Values | | D | Values | | F | Values |
|----------------| |----------------| |----------------| |----------------| |----------------| |----------------|
| True | ###### | | True | 0.1434 | | True | 0.4403 | | True | 0.5426 | | True | 0.2780 | | True | ###### |
| False | ###### | | False | 0.8566 | | False | 0.5597 | | False | 0.4574 | | False | 0.7220 | | False | ###### |
------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 2): Err(EDF) = 0.0169.
------------------ ------------------ ------------------ ~~~~ AD = 0.0429 / ~~~~ AD = 0.0025 / ~~~~ AD = 0.0048 /
| A | Values | | C | Values | | B | Values | / E / Values / / D / Values / / F / Values /
|----------------| |----------------| |----------------| /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/
| True | ###### | | True | ###### | | True | ###### | / True / 0.4820 / / True / 0.2745 / / True / 0.2969 /
| False | ###### | | False | ###### | | False | ###### | / False / 0.5180 / / False / 0.7255 / / False / 0.7031 /
------------------ ------------------ ------------------ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
Enter a command (enter h + [Enter] for help):
Indicates that subnet does not represent this variable
Indicates that marginal variable distribution differs from “true marginal”
Shows average discrapancy between subnet marginals and “true marginals”
Shows average discrepancy between subnet and true joint distributions of the variables of the subnet
Indicates that marginal variable distribution matches “true marginal”
58
MatLab Tool: ControlMatLab Tool: ControlEnter a command (enter h + [Enter] for help): hType:
i + [Enter] to Initialize, v + [Enter] to view all variables (even those containing no information),e + [Enter] to enter evidence, c + [Enter] to perform a inter-subnet communication,
p + [Enter] to go to the previous step, n + [Enter] to go to the next step,
a + [Enter] to add a sensor, r + [Enter] to remove a sensor,t + [Enter] to turn true marginals view OFF, m + [Enter] to turn discrepancy marking OFF,s + [Enter] to save to a file, q + [Enter] to quit.
So, what do you want to do?
59
MatLab Tool: Initial stateMatLab Tool: Initial state * Configuration 1: Initial configuration:
SUBNET 1 (adjacent to subnets 2, 3, 4, 5): ------------------ ------------------ ------------------ ------------------ ------------------ ------------------ | CT | Values | | RF1 | Values | | RF2 | Values | | CF3 | Values | | CM7 | Values | | RF5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.0069 | | True | 0.8064 | | True | 0.6287 | | True | 0.5420 | | True | 0.2257 | | True | 0.4738 | | False | 0.9931 | | False | 0.1936 | | False | 0.3713 | | False | 0.4580 | | False | 0.7743 | | False | 0.5262 | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1): ------------------ ------------------ ------------------ | CM7 | Values | | RM8 | Values | | RF5 | Values | |----------------| |----------------| |----------------| | True | 0.2257 | | True | 0.8332 | | True | 0.4738 | | False | 0.7743 | | False | 0.1668 | | False | 0.5262 | ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ ------------------ | CF3 | Values | | RF5 | Values | | RF4 | Values | | RM6 | Values | | RM5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.5420 | | True | 0.4738 | | True | 0.4616 | | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | | False | 0.5262 | | False | 0.5384 | | False | 0.5000 | | False | 0.7798 | ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM1 | Values | | RM2 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8064 | | True | 0.6287 | | True | 0.2472 | | True | 0.5120 | | False | 0.1936 | | False | 0.3713 | | False | 0.7528 | | False | 0.4880 | ------------------ ------------------ ------------------ ------------------
SUBNET 5 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM3 | Values | | RM4 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8064 | | True | 0.6287 | | True | 0.4481 | | True | 0.3351 | | False | 0.1936 | | False | 0.3713 | | False | 0.5519 | | False | 0.6649 | ------------------ ------------------ ------------------ ------------------
60
MatLab Tool: Initial stateMatLab Tool: Initial state * Configuration 1: Initial configuration:
SUBNET 1 (adjacent to subnets 2, 3, 4, 5): ------------------ ------------------ ------------------ ------------------ ------------------ ------------------ | CT | Values | | RF1 | Values | | RF2 | Values | | CF3 | Values | | CM7 | Values | | RF5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.0069 | | True | 0.8064 | | True | 0.6287 | | True | 0.5420 | | True | 0.2257 | | True | 0.4738 | | False | 0.9931 | | False | 0.1936 | | False | 0.3713 | | False | 0.4580 | | False | 0.7743 | | False | 0.5262 | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1): ------------------ ------------------ ------------------ | CM7 | Values | | RM8 | Values | | RF5 | Values | |----------------| |----------------| |----------------| | True | 0.2257 | | True | 0.8332 | | True | 0.4738 | | False | 0.7743 | | False | 0.1668 | | False | 0.5262 | ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ ------------------ | CF3 | Values | | RF5 | Values | | RF4 | Values | | RM6 | Values | | RM5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.5420 | | True | 0.4738 | | True | 0.4616 | | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | | False | 0.5262 | | False | 0.5384 | | False | 0.5000 | | False | 0.7798 | ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM1 | Values | | RM2 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8064 | | True | 0.6287 | | True | 0.2472 | | True | 0.5120 | | False | 0.1936 | | False | 0.3713 | | False | 0.7528 | | False | 0.4880 | ------------------ ------------------ ------------------ ------------------
SUBNET 5 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM3 | Values | | RM4 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8064 | | True | 0.6287 | | True | 0.4481 | | True | 0.3351 | | False | 0.1936 | | False | 0.3713 | | False | 0.5519 | | False | 0.6649 | ------------------ ------------------ ------------------ ------------------
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
RF1
RM3RM4
RF2
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
2345
61
MatLab Tool: Remove a sensorMatLab Tool: Remove a sensor * Configuration 2: The radar-subnet number 5 was removed.
SUBNET 1 (adjacent to subnets 2, 3, 4): ------------------ ------------------ ------------------ ------------------ ------------------ ------------------ | CT | Values | | RF1 | Values | | RF2 | Values | | CF3 | Values | | CM7 | Values | | RF5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.0069 | | True | 0.8064 | | True | 0.6287 | | True | 0.5420 | | True | 0.2257 | | True | 0.4738 | | False | 0.9931 | | False | 0.1936 | | False | 0.3713 | | False | 0.4580 | | False | 0.7743 | | False | 0.5262 | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1): ------------------ ------------------ ------------------ | CM7 | Values | | RM8 | Values | | RF5 | Values | |----------------| |----------------| |----------------| | True | 0.2257 | | True | 0.8332 | | True | 0.4738 | | False | 0.7743 | | False | 0.1668 | | False | 0.5262 | ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ ------------------ | CF3 | Values | | RF5 | Values | | RF4 | Values | | RM6 | Values | | RM5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.5420 | | True | 0.4738 | | True | 0.4616 | | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | | False | 0.5262 | | False | 0.5384 | | False | 0.5000 | | False | 0.7798 | ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM1 | Values | | RM2 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8064 | | True | 0.6287 | | True | 0.2472 | | True | 0.5120 | | False | 0.1936 | | False | 0.3713 | | False | 0.7528 | | False | 0.4880 | ------------------ ------------------ ------------------ ------------------
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
234
62
MatLab Tool: Receive evidenceMatLab Tool: Receive evidenceEnter a command (enter h + [Enter] for help): e
In which subnet (number) do you wish to insert evidence? 2
The variables handled by subnet number 2 of this cell are: 5: CM7 6: RM8 7: RF5 Which variable NUMBER does the evidence pertain to? 6
Enter likelihood for state "True": 0
Enter likelihood for state "False": 1
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
234
Subnet 2 receives evidence on RM8.
63
MatLab Tool: Receive evidenceMatLab Tool: Receive evidence * Configuration 3: After evidence L(e|RM8) = (0,1) has been entered into subnet number 2
SUBNET 1 (adjacent to subnets 2, 3, 4): Err(CTCF3RF5) = 0.0368. Err(CTCM7RF5) = 0.0395. ------------------ ------------------ ------------------ ------------------ ------------------ ~~~~ AD = 0.0784 / | CT | Values | | RF1 | Values | | RF2 | Values | | CF3 | Values | | CM7 | Values | / RF5 / Values / |----------------| |----------------| |----------------| |----------------| |----------------| /~~~~~~~~~~~~~~~~/ | True | 0.0069 | | True | 0.8064 | | True | 0.6287 | | True | 0.5420 | | True | 0.2257 | / True / 0.4738 / | False | 0.9931 | | False | 0.1936 | | False | 0.3713 | | False | 0.4580 | | False | 0.7743 | / False / 0.5262 / ------------------ ------------------ ------------------ ------------------ ------------------ ~~~~~~~~~~~~~~~~~~
SUBNET 2 (adjacent to subnets 1): ------------------ ------------------ ------------------ | CM7 | Values | | RM8 | Values | | RF5 | Values | |----------------| |----------------| |----------------| | True | 0.2257 | | True | 0.0000 | | True | 0.3629 | | False | 0.7743 | | False | 1.0000 | | False | 0.6371 | ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): Err(CF3RM5RF5RF4) = 0.0169. Err(RF5RM6) = 0.0555. ------------------ ~~~~ AD = 0.0784 / ~~~~ AD = 0.0119 / ------------------ ------------------ | CF3 | Values | / RF5 / Values / / RF4 / Values / | RM6 | Values | | RM5 | Values | |----------------| /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ |----------------| |----------------| | True | 0.5420 | / True / 0.4738 / / True / 0.4616 / | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | / False / 0.5262 / / False / 0.5384 / | False | 0.5000 | | False | 0.7798 | ------------------ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM1 | Values | | RM2 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8064 | | True | 0.6287 | | True | 0.2472 | | True | 0.5120 | | False | 0.1936 | | False | 0.3713 | | False | 0.7528 | | False | 0.4880 | ------------------ ------------------ ------------------ ------------------
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
234
64
MatLab Tool: Receive evidenceMatLab Tool: Receive evidenceEnter a command (enter h + [Enter] for help): e
In which subnet (number) do you wish to insert evidence? 4
The variables handled by subnet number 4 of this cell are: 2: RF1 3: RF2 11: RM1 12: RM2 Which variable NUMBER does the evidence pertain to? 12
Enter likelihood for state "True": 3
Enter likelihood for state "False": 5
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
234
Subnet 4 receives evidence on RM2.
65
MatLab Tool: Receive evidenceMatLab Tool: Receive evidence * Configuration 4: After evidence L(e|RM2) = (3,5) has been entered into subnet number 4
SUBNET 1 (adjacent to subnets 2, 3, 4): Err(CTRF1RF2) = 0.0059. Err(CTCF3RF5) = 0.0368. Err(CTCM7RF5) = 0.0395. ------------------ ~~~~ AD = 0.0012 / ~~~~ AD = 0.0063 / ------------------ ------------------ ~~~~ AD = 0.0784 / | CT | Values | / RF1 / Values / / RF2 / Values / | CF3 | Values | | CM7 | Values | / RF5 / Values / |----------------| /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ |----------------| |----------------| /~~~~~~~~~~~~~~~~/ | True | 0.0069 | / True / 0.8064 / / True / 0.6287 / | True | 0.5420 | | True | 0.2257 | / True / 0.4738 / | False | 0.9931 | / False / 0.1936 / / False / 0.3713 / | False | 0.4580 | | False | 0.7743 | / False / 0.5262 / ------------------ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ------------------ ------------------ ~~~~~~~~~~~~~~~~~~
SUBNET 2 (adjacent to subnets 1): ------------------ ------------------ ------------------ | CM7 | Values | | RM8 | Values | | RF5 | Values | |----------------| |----------------| |----------------| | True | 0.2257 | | True | 0.0000 | | True | 0.3629 | | False | 0.7743 | | False | 1.0000 | | False | 0.6371 | ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): Err(CF3RM5RF5RF4) = 0.0169. Err(RF5RM6) = 0.0555. ------------------ ~~~~ AD = 0.0784 / ~~~~ AD = 0.0119 / ------------------ ------------------ | CF3 | Values | / RF5 / Values / / RF4 / Values / | RM6 | Values | | RM5 | Values | |----------------| /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ |----------------| |----------------| | True | 0.5420 | / True / 0.4738 / / True / 0.4616 / | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | / False / 0.5262 / / False / 0.5384 / | False | 0.5000 | | False | 0.7798 | ------------------ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM1 | Values | | RM2 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8081 | | True | 0.6376 | | True | 0.2633 | | True | 0.3863 | | False | 0.1919 | | False | 0.3624 | | False | 0.7367 | | False | 0.6137 | ------------------ ------------------ ------------------ ------------------
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
234
66
* Configuration 5: After subnet 4 sent information to subnet 1
SUBNET 1 (adjacent to subnets 2, 3, 4): Err(CTCF3RF5) = 0.0368. Err(CTCM7RF5) = 0.0395. ------------------ ------------------ ------------------ ------------------ ------------------ ~~~~ AD = 0.0784 / | CT | Values | | RF1 | Values | | RF2 | Values | | CF3 | Values | | CM7 | Values | / RF5 / Values / |----------------| |----------------| |----------------| |----------------| |----------------| /~~~~~~~~~~~~~~~~/ | True | 0.0068 | | True | 0.8081 | | True | 0.6376 | | True | 0.5420 | | True | 0.2257 | / True / 0.4738 / | False | 0.9932 | | False | 0.1919 | | False | 0.3624 | | False | 0.4580 | | False | 0.7743 | / False / 0.5262 / ------------------ ------------------ ------------------ ------------------ ------------------ ~~~~~~~~~~~~~~~~~~
SUBNET 2 (adjacent to subnets 1): ------------------ ------------------ ------------------ | CM7 | Values | | RM8 | Values | | RF5 | Values | |----------------| |----------------| |----------------| | True | 0.2257 | | True | 0.0000 | | True | 0.3629 | | False | 0.7743 | | False | 1.0000 | | False | 0.6371 | ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): Err(CF3RM5RF5RF4) = 0.0169. Err(RF5RM6) = 0.0555. ------------------ ~~~~ AD = 0.0784 / ~~~~ AD = 0.0119 / ------------------ ------------------ | CF3 | Values | / RF5 / Values / / RF4 / Values / | RM6 | Values | | RM5 | Values | |----------------| /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ |----------------| |----------------| | True | 0.5420 | / True / 0.4738 / / True / 0.4616 / | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | / False / 0.5262 / / False / 0.5384 / | False | 0.5000 | | False | 0.7798 | ------------------ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM1 | Values | | RM2 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8081 | | True | 0.6376 | | True | 0.2633 | | True | 0.3863 | | False | 0.1919 | | False | 0.3624 | | False | 0.7367 | | False | 0.6137 | ------------------ ------------------ ------------------ ------------------
MatLab Tool: Subnet communicationMatLab Tool: Subnet communication
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
234Enter a command (enter h + [Enter] for help): c Send information FROM subnet number: 4 Subnet 4 can communicate with the following subnets: 1 Enter the subnet number that subnet 4 should send information
TO: 1
67
* Configuration 6: After subnet 2 sent information to subnet 1
SUBNET 1 (adjacent to subnets 2, 3, 4): ------------------ ------------------ ------------------ ------------------ ------------------ ------------------ | CT | Values | | RF1 | Values | | RF2 | Values | | CF3 | Values | | CM7 | Values | | RF5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.0068 | | True | 0.8081 | | True | 0.6376 | | True | 0.5420 | | True | 0.2257 | | True | 0.3628 | | False | 0.9932 | | False | 0.1919 | | False | 0.3624 | | False | 0.4580 | | False | 0.7743 | | False | 0.6372 | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1): ------------------ ------------------ ------------------ | CM7 | Values | | RM8 | Values | | RF5 | Values | |----------------| |----------------| |----------------| | True | 0.2257 | | True | 0.0000 | | True | 0.3629 | | False | 0.7743 | | False | 1.0000 | | False | 0.6371 | ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): Err(CF3RM5RF5RF4) = 0.0169. Err(RF5RM6) = 0.0555. ------------------ ~~~~ AD = 0.0784 / ~~~~ AD = 0.0119 / ------------------ ------------------ | CF3 | Values | / RF5 / Values / / RF4 / Values / | RM6 | Values | | RM5 | Values | |----------------| /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ |----------------| |----------------| | True | 0.5420 | / True / 0.4738 / / True / 0.4616 / | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | / False / 0.5262 / / False / 0.5384 / | False | 0.5000 | | False | 0.7798 | ------------------ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM1 | Values | | RM2 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8081 | | True | 0.6376 | | True | 0.2633 | | True | 0.3863 | | False | 0.1919 | | False | 0.3624 | | False | 0.7367 | | False | 0.6137 | ------------------ ------------------ ------------------ ------------------
MatLab Tool: Subnet communicationMatLab Tool: Subnet communication
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
234Enter a command (enter h + [Enter] for help): c Send information FROM subnet number: 2 Subnet 4 can communicate with the following subnets: 1 Enter the subnet number that subnet 4 should send information
TO: 1
68
* Configuration 7: After subnet 1 sent information to subnet 3
SUBNET 1 (adjacent to subnets 2, 3, 4): ------------------ ------------------ ------------------ ------------------ ------------------ ------------------ | CT | Values | | RF1 | Values | | RF2 | Values | | CF3 | Values | | CM7 | Values | | RF5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.0068 | | True | 0.8081 | | True | 0.6376 | | True | 0.5420 | | True | 0.2257 | | True | 0.3628 | | False | 0.9932 | | False | 0.1919 | | False | 0.3624 | | False | 0.4580 | | False | 0.7743 | | False | 0.6372 | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1): ------------------ ------------------ ------------------ | CM7 | Values | | RM8 | Values | | RF5 | Values | |----------------| |----------------| |----------------| | True | 0.2257 | | True | 0.0000 | | True | 0.3629 | | False | 0.7743 | | False | 1.0000 | | False | 0.6371 | ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ ------------------ | CF3 | Values | | RF5 | Values | | RF4 | Values | | RM6 | Values | | RM5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.5420 | | True | 0.3628 | | True | 0.4784 | | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | | False | 0.6372 | | False | 0.5216 | | False | 0.5000 | | False | 0.7798 | ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM1 | Values | | RM2 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8081 | | True | 0.6376 | | True | 0.2633 | | True | 0.3863 | | False | 0.1919 | | False | 0.3624 | | False | 0.7367 | | False | 0.6137 | ------------------ ------------------ ------------------ ------------------
MatLab Tool: Subnet communicationMatLab Tool: Subnet communication
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
234Enter a command (enter h + [Enter] for help): c Send information FROM subnet number: 1 Subnet 4 can communicate with the following subnets: 2, 3, 4 Enter the subnet number that subnet 4 should send information TO:
3
69
MatLab Tool: Add a subnetMatLab Tool: Add a subnet * Configuration 8: The radar-subnet number 5 was added.
SUBNET 1 (adjacent to subnets 2, 3, 4, 5): Err(CTRF1RF2) = 0.0227. Err(CTCF3RF5) = 0.0004. Err(CTCM7RF5) = 0.0004. ~~~~ AD = 0.0011 / ~~~~ AD = 0.0464 / ~~~~ AD = 0.0087 / ------------------ ~~~~ AD = 0.0002 / ------------------ / CT / Values / / RF1 / Values / / RF2 / Values / | CF3 | Values | / CM7 / Values / | RF5 | Values | /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ |----------------| /~~~~~~~~~~~~~~~~/ |----------------| / True / 0.0068 / / True / 0.8081 / / True / 0.6376 / | True | 0.5420 | / True / 0.2257 / | True | 0.3628 | / False / 0.9932 / / False / 0.1919 / / False / 0.3624 / | False | 0.4580 | / False / 0.7743 / | False | 0.6372 | ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ------------------ ~~~~~~~~~~~~~~~~~~ ------------------
SUBNET 2 (adjacent to subnets 1): Err(CM7RM8RF5) = 0.0001. ~~~~ AD = 0.0002 / ------------------ ------------------ / CM7 / Values / | RM8 | Values | | RF5 | Values | /~~~~~~~~~~~~~~~~/ |----------------| |----------------| / True / 0.2257 / | True | 0.0000 | | True | 0.3629 | / False / 0.7743 / | False | 1.0000 | | False | 0.6371 | ~~~~~~~~~~~~~~~~~~ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ ------------------ | CF3 | Values | | RF5 | Values | | RF4 | Values | | RM6 | Values | | RM5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.5420 | | True | 0.3628 | | True | 0.4784 | | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | | False | 0.6372 | | False | 0.5216 | | False | 0.5000 | | False | 0.7798 | ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): Err(RF1RF2RM1RM2) = 0.0099. ~~~~ AD = 0.0464 / ~~~~ AD = 0.0087 / ~~~~ AD = 0.0009 / ~~~~ AD = 0.0011 / / RF1 / Values / / RF2 / Values / / RM1 / Values / / RM2 / Values / /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ / True / 0.8081 / / True / 0.6376 / / True / 0.2633 / / True / 0.3863 / / False / 0.1919 / / False / 0.3624 / / False / 0.7367 / / False / 0.6137 / ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
SUBNET 5 (adjacent to subnets 1): Err(RF1RF2RM3RM4) = 0.2284. ~~~~ AD = 0.1826 / ~~~~ AD = 0.1091 / ~~~~ AD = 0.0122 / ~~~~ AD = 0.0123 / / RF1 / Values / / RF2 / Values / / RM3 / Values / / RM4 / Values / /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ / True / 0.6154 / / True / 0.4710 / / True / 0.1905 / / True / 0.5625 / / False / 0.3846 / / False / 0.5290 / / False / 0.8095 / / False / 0.4375 / ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
RF1
RM3RM4
RF2
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
2345
Enter a command (enter h + [Enter] for help): a
70
MatLab Tool: Subnet communicationMatLab Tool: Subnet communication * Configuration 9: After subnet 5 sent information to subnet 1
SUBNET 1 (adjacent to subnets 2, 3, 4, 5): ------------------ ------------------ ------------------ ------------------ ------------------ ------------------ | CT | Values | | RF1 | Values | | RF2 | Values | | CF3 | Values | | CM7 | Values | | RF5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.0052 | | True | 0.8736 | | True | 0.6253 | | True | 0.5419 | | True | 0.2254 | | True | 0.3628 | | False | 0.9948 | | False | 0.1264 | | False | 0.3747 | | False | 0.4581 | | False | 0.7746 | | False | 0.6372 | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1): Err(CM7RM8RF5) = 0.0001. ~~~~ AD = 0.0002 / ------------------ ------------------ / CM7 / Values / | RM8 | Values | | RF5 | Values | /~~~~~~~~~~~~~~~~/ |----------------| |----------------| / True / 0.2257 / | True | 0.0000 | | True | 0.3629 | / False / 0.7743 / | False | 1.0000 | | False | 0.6371 | ~~~~~~~~~~~~~~~~~~ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ ------------------ | CF3 | Values | | RF5 | Values | | RF4 | Values | | RM6 | Values | | RM5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.5420 | | True | 0.3628 | | True | 0.4784 | | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | | False | 0.6372 | | False | 0.5216 | | False | 0.5000 | | False | 0.7798 | ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): Err(RF1RF2RM1RM2) = 0.0099. ~~~~ AD = 0.0464 / ~~~~ AD = 0.0087 / ~~~~ AD = 0.0009 / ~~~~ AD = 0.0011 / / RF1 / Values / / RF2 / Values / / RM1 / Values / / RM2 / Values / /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ / True / 0.8081 / / True / 0.6376 / / True / 0.2633 / / True / 0.3863 / / False / 0.1919 / / False / 0.3624 / / False / 0.7367 / / False / 0.6137 / ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
SUBNET 5 (adjacent to subnets 1): Err(RF1RF2RM3RM4) = 0.2284. ~~~~ AD = 0.1826 / ~~~~ AD = 0.1091 / ~~~~ AD = 0.0122 / ~~~~ AD = 0.0123 / / RF1 / Values / / RF2 / Values / / RM3 / Values / / RM4 / Values / /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ / True / 0.6154 / / True / 0.4710 / / True / 0.1905 / / True / 0.5625 / / False / 0.3846 / / False / 0.5290 / / False / 0.8095 / / False / 0.4375 / ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
RF1
RM3RM4
RF2
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
2345
71
MatLab Tool: Subnet communicationMatLab Tool: Subnet communication * Configuration 10: After subnet 1 sent information to subnet 2
SUBNET 1 (adjacent to subnets 2, 3, 4, 5): ------------------ ------------------ ------------------ ------------------ ------------------ ------------------ | CT | Values | | RF1 | Values | | RF2 | Values | | CF3 | Values | | CM7 | Values | | RF5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.0052 | | True | 0.8736 | | True | 0.6253 | | True | 0.5419 | | True | 0.2254 | | True | 0.3628 | | False | 0.9948 | | False | 0.1264 | | False | 0.3747 | | False | 0.4581 | | False | 0.7746 | | False | 0.6372 | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1): ------------------ ------------------ ------------------ | CM7 | Values | | RM8 | Values | | RF5 | Values | |----------------| |----------------| |----------------| | True | 0.2254 | | True | 0.0000 | | True | 0.3628 | | False | 0.7746 | | False | 1.0000 | | False | 0.6372 | ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ ------------------ | CF3 | Values | | RF5 | Values | | RF4 | Values | | RM6 | Values | | RM5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.5420 | | True | 0.3628 | | True | 0.4784 | | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | | False | 0.6372 | | False | 0.5216 | | False | 0.5000 | | False | 0.7798 | ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): Err(RF1RF2RM1RM2) = 0.0099. ~~~~ AD = 0.0464 / ~~~~ AD = 0.0087 / ~~~~ AD = 0.0009 / ~~~~ AD = 0.0011 / / RF1 / Values / / RF2 / Values / / RM1 / Values / / RM2 / Values / /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ / True / 0.8081 / / True / 0.6376 / / True / 0.2633 / / True / 0.3863 / / False / 0.1919 / / False / 0.3624 / / False / 0.7367 / / False / 0.6137 / ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
SUBNET 5 (adjacent to subnets 1): Err(RF1RF2RM3RM4) = 0.2284. ~~~~ AD = 0.1826 / ~~~~ AD = 0.1091 / ~~~~ AD = 0.0122 / ~~~~ AD = 0.0123 / / RF1 / Values / / RF2 / Values / / RM3 / Values / / RM4 / Values / /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ / True / 0.6154 / / True / 0.4710 / / True / 0.1905 / / True / 0.5625 / / False / 0.3846 / / False / 0.5290 / / False / 0.8095 / / False / 0.4375 / ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
RF1
RM3RM4
RF2
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
2345
72
MatLab Tool: Subnet communicationMatLab Tool: Subnet communication * Configuration 11: After subnet 1 sent information to subnet 4
SUBNET 1 (adjacent to subnets 2, 3, 4, 5): ------------------ ------------------ ------------------ ------------------ ------------------ ------------------ | CT | Values | | RF1 | Values | | RF2 | Values | | CF3 | Values | | CM7 | Values | | RF5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.0052 | | True | 0.8736 | | True | 0.6253 | | True | 0.5419 | | True | 0.2254 | | True | 0.3628 | | False | 0.9948 | | False | 0.1264 | | False | 0.3747 | | False | 0.4581 | | False | 0.7746 | | False | 0.6372 | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1): ------------------ ------------------ ------------------ | CM7 | Values | | RM8 | Values | | RF5 | Values | |----------------| |----------------| |----------------| | True | 0.2254 | | True | 0.0000 | | True | 0.3628 | | False | 0.7746 | | False | 1.0000 | | False | 0.6372 | ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ ------------------ | CF3 | Values | | RF5 | Values | | RF4 | Values | | RM6 | Values | | RM5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.5420 | | True | 0.3628 | | True | 0.4784 | | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | | False | 0.6372 | | False | 0.5216 | | False | 0.5000 | | False | 0.7798 | ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM1 | Values | | RM2 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8736 | | True | 0.6253 | | True | 0.2645 | | True | 0.3848 | | False | 0.1264 | | False | 0.3747 | | False | 0.7355 | | False | 0.6152 | ------------------ ------------------ ------------------ ------------------
SUBNET 5 (adjacent to subnets 1): Err(RF1RF2RM3RM4) = 0.2284. ~~~~ AD = 0.1826 / ~~~~ AD = 0.1091 / ~~~~ AD = 0.0122 / ~~~~ AD = 0.0123 / / RF1 / Values / / RF2 / Values / / RM3 / Values / / RM4 / Values / /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ /~~~~~~~~~~~~~~~~/ / True / 0.6154 / / True / 0.4710 / / True / 0.1905 / / True / 0.5625 / / False / 0.3846 / / False / 0.5290 / / False / 0.8095 / / False / 0.4375 / ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
RF1
RM3RM4
RF2
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
2345
73
MatLab Tool: Subnet communicationMatLab Tool: Subnet communication * Configuration 12: After subnet 1 sent information to subnet 5
SUBNET 1 (adjacent to subnets 2, 3, 4, 5): ------------------ ------------------ ------------------ ------------------ ------------------ ------------------ | CT | Values | | RF1 | Values | | RF2 | Values | | CF3 | Values | | CM7 | Values | | RF5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.0052 | | True | 0.8736 | | True | 0.6253 | | True | 0.5419 | | True | 0.2254 | | True | 0.3628 | | False | 0.9948 | | False | 0.1264 | | False | 0.3747 | | False | 0.4581 | | False | 0.7746 | | False | 0.6372 | ------------------ ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 2 (adjacent to subnets 1): ------------------ ------------------ ------------------ | CM7 | Values | | RM8 | Values | | RF5 | Values | |----------------| |----------------| |----------------| | True | 0.2254 | | True | 0.0000 | | True | 0.3628 | | False | 0.7746 | | False | 1.0000 | | False | 0.6372 | ------------------ ------------------ ------------------
SUBNET 3 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ ------------------ | CF3 | Values | | RF5 | Values | | RF4 | Values | | RM6 | Values | | RM5 | Values | |----------------| |----------------| |----------------| |----------------| |----------------| | True | 0.5420 | | True | 0.3628 | | True | 0.4784 | | True | 0.5000 | | True | 0.2202 | | False | 0.4580 | | False | 0.6372 | | False | 0.5216 | | False | 0.5000 | | False | 0.7798 | ------------------ ------------------ ------------------ ------------------ ------------------
SUBNET 4 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM1 | Values | | RM2 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8736 | | True | 0.6253 | | True | 0.2645 | | True | 0.3848 | | False | 0.1264 | | False | 0.3747 | | False | 0.7355 | | False | 0.6152 | ------------------ ------------------ ------------------ ------------------
SUBNET 5 (adjacent to subnets 1): ------------------ ------------------ ------------------ ------------------ | RF1 | Values | | RF2 | Values | | RM3 | Values | | RM4 | Values | |----------------| |----------------| |----------------| |----------------| | True | 0.8736 | | True | 0.6253 | | True | 0.1733 | | True | 0.5451 | | False | 0.1264 | | False | 0.3747 | | False | 0.8267 | | False | 0.4549 | ------------------ ------------------ ------------------ ------------------
CTCF3
CT
RF5
CTRF1
RF2RF1
RF5RF2
RM1RM2
RM6
RM8
RF1
RM3RM4
RF2
CM7
CM7RF5CF3
RF5RF4RM5
RF4
1
2345